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Assign two variables for each problem, and write the equations. Do not solve.

The Math Club is having their end-of-the-year party. Natasha found that the cafeteria usually makes 200 cups of pineapple-ginger ale fruit punch. The cook told her that if she doubles the pineapple and triples the ginger ale, she will have a total of 420 cups of punch. How many cups of each are needed to make 420 cups of fruit punch?

Respuesta :

twvogels
Call the amount of pineapple "P', and the amount of gingerale "G".

We know that a mix of pineapple and gingerale makes 200 cups. So: 
[tex] P+G=200 [/tex]

We also know that double the pineapple (i.e. 2P) and triple the gingerale (i.e. 3G) makes 420 cups. So:
[tex] 2P+3G=420[/tex]

We can now solve by substitution:
[tex] 2P+3(200-P)=420[/tex]
[tex]2P+600-3P=420[/tex]
[tex]-P=-180[/tex]
[tex]P=180[/tex]

[tex]180+G=200[/tex]
[tex]G=20[/tex]

For 420 cups we need 2P=360 cups of pineapple and 3G=60 cups of gingerale]

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